Finite Group Databasebeta

← #13078146

Subgroups — #13078146

Order 1408.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#519C211yesmaximal, characteristic, complemented
2C22×#4326C211yesmaximal, characteristic, complemented
3C2×#66995C211yesmaximal, characteristic
4#10623057C211yesmaximal, characteristic
5#10622644C214yesmaximal, complemented
6#10622641C214yesmaximal, complemented
7#10622617C211yesmaximal, characteristic, complemented
8#10622615C211yesmaximal, characteristic
9#10622612C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2211yescharacteristic
11C2×#4339C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C4×Q8×C11—22no—
14C4×Q8×C11C2214yes—
15C11×#117—22no—
16C11×#117C2211yescharacteristic
17C11×#117C2211yescharacteristic
18C2×#4326—24no—
19C2×#4326C2212yes—
20C2×#4326C2214yes—
21#66995—24no—
22C2×#4325C2212yes—
23C2×#4318C2211yescharacteristic
24C22×C11⋊C8C2211yescharacteristic
25#66950—22no—
26#66939—22no—
27#66928C2212yes—
28#66922C2212yes—
29#66874C2212yes—
30#66874C2214yes—
31#66873C2212yes—
32C4⋊(C11⋊C8)C2214yes—
33C2×Q8×C11—21no—
34C2×Q8×C11—22no—
35C2×Q8×C11D414yes—
36C2×Q8×C11C2312yes—
37C22×C4×C11—21no—
38C22×C4×C11C2311yescharacteristic
39C2×C22⋊D11—21no—
40C22×Dic11—21no—
41#4339—22no—
42#4339—22no—
43C2×D44C2311yescharacteristic
44C2×C4×D11—21no—
45C2×Dic22—22no—
46C2×Dic22—21no—
47C2×Dic22—22no—
48C2×Dic22C2311yescharacteristic
49C2×Dic22C2312yes—
50C11×C4⋊C4—24no—
51C11×C4⋊C4D412yes—
52C11×C4⋊C4C2312yes—
53C11×C22⋊C4—21no—
54C11×C22⋊C4D412yes—
55C42×C11—24no—
56C42×C11—21no—
57C42×C11C2312yes—
58#4326—24no—
59#4326—28no—
60#4325—24no—
61(C2×D11)⋊C4—24no—
62C4⋊Dic11—24no—
63#4318—22no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8C2312yes—
66C2×C11⋊C8C2312yes—
67#3044—111nomaximal, Sylow
68C23×C11C2×D411yescharacteristic
69C22×D11—21no—
70Q8×C11—24no—
71Q8×C11—22no—
72Q8×C11C2×D414yes—
73C2×C4×C11—24no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D414yes—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11#4112yes—
80C2×C4×C11C2411yescharacteristic
81C22⋊D11—42no—
82C2×Dic11—21no—
83C2×Dic11—22no—
84C2×Dic11—42no—
85D44—21no—
86D44—21no—
87C4×D11—42no—
88Dic22—22no—
89Dic22—21no—
90Dic22—22no—
91Dic22—21no—
92Dic22—42no—
93C11⋊C8—22no—
94C11⋊C8—22no—
95C2×#137—111no—
96C22×Q16—111no—
97#536—111no—
98#519D1111yescharacteristic, complemented
99#464—114no—
100#462—114no—
101#424—111no—
102#419—111no—
103#416—111no—
104C22×C11—22no—
105C22×C11#12112yes—
106C22×C11C22×D411yescharacteristic
107C2×D11—41no—
108C2×D11—42no—
109C4×C11—24no—
110C4×C11—24no—
111C4×C11—42no—
112C4×C11#12112yes—
113C4×C11C22×D411yescharacteristic
114C4×C11C2×#4111yescharacteristic
115Dic11—42no—
116Dic11—41no—
117C2×#41—111no—
118C22×Q8—111no—
119C22×Q8C2×D1111yescharacteristic
120#137—224no—
121C2×Q16—114no—
122C2×Q16—112no—
123C2×Q16—224no—
124C2×SD16—112no—
125C2×M16—111no—
126C22×C8—111no—
127C4⋊Q8—112no—
128#124—112no—
129#123—222no—
130C22⋊Q8—222no—
131C4×Q8—22no—
132C4×Q8C2×D1114yes—
133#117—22no—
134#117C2×D1111yescharacteristic
135#117C2×D1111yescharacteristic
136C4⋊C8—114no—
137#103—112no—
138#103—114no—
139#102—112no—
140C2×C11—22no—
141C2×C11C2×#12111yescharacteristic
142C2×C11#57812yes—
143D11—81no—
144#41—222no—
145#41—222no—
146C2×Q8—22no—
147C2×Q8—21no—
148C2×Q8—112no—
149C2×Q8—111no—
150C2×Q8—221no—
151C2×Q8—222no—
152C2×Q8—222no—
153C2×Q8D4414yes—
154C2×Q8C22×D1112yes—
155C2×D4—111no—
156C2×D4—221no—
157C22×C4—21no—
158C22×C4—221no—
159C22×C4—221no—
160C22×C4C22×D1111yescharacteristic
161Q16—228no—
162Q16—224no—
163SD16—224no—
164M16—222no—
165C2×C8—112no—
166C2×C8—112no—
167C2×C8—222no—
168C4⋊C4—24no—
169C4⋊C4—224no—
170C4⋊C4C22⋊D1112yes—
171C4⋊C4C22×D1112yes—
172C22⋊C4—21no—
173C22⋊C4—224no—
174C22⋊C4C22⋊D1112yes—
175C42—24no—
176C42—21no—
177C42C22×D1112yes—
178C11#304411yescharacteristic, complemented, Sylow
179C23—221no—
180C23C2×C22⋊D1111yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—222no—
184Q8—221no—
185Q8—222no—
186Q8—221no—
187Q8—442no—
188Q8C2×D4414yes—
189D4—221no—
190D4—221no—
191D4—442no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—222no—
196C2×C4—221no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4C2×D4412yes—
200C2×C4#433912yes—
201C2×C4C2×C22⋊D1114yes—
202C2×C4C2×C22⋊D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—222no—
205C8—222no—
206C22—22no—
207C22—441no—
208C22—442no—
209C22#6698312yes—
210C22C22×C22⋊D1111yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—441no—
215C4—442no—
216C4#6698312yes—
217C4C22×D4411yescharacteristic
218C4C2×#433911yescharacteristic
219C2—22no—
220C2—881no—
221C2C2×#6698311yescharacteristic
222C2#1062336912yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#519C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#519D11
hypocenterC11#3044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#519C2semidirect
2. C22×#4326C2semidirect
5. #10622644C2semidirect
6. #10622641C2semidirect
7. #10622617C2semidirect
9. #10622612C2semidirect
98. #519D11semidirect
178. C11#3044semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#5192
C22×#43262
C2×#669952
#106230572
#106226442
#106226412
#106226172
#106226152
#106226122
#304411